Social Learning with Model Misspeciﬁcation: A Framework and a Characterization
This paper develops a general framework to study how misinterpreting in-formation impacts learning. We consider sequential social learning and passive individual learning settings in which individuals observe signals and the actions of predecessors. Individuals have incorrect, or misspeciﬁed models of how to in-terpret these sources – such as overreaction to signals or misperception of others’ preferences. Our main result is a simple criterion to characterize long-run beliefs and behavior based on the underlying form of misspeciﬁcation. This provides a uniﬁed way to compare diﬀerent forms of misspeciﬁcation that have been previ-ously studied, as well as generates new insights about forms of misspeciﬁcation that have not been theoretically explored. It allows for a deeper understanding of how misspeciﬁcation impacts learning, including exploring whether a given form of misspeciﬁcation is conceptually robust, in that it is not sensitive to parametric speciﬁcation, whether misspeciﬁcation has a similar impact in individual and so-cial learning settings, and how model heterogeneity impacts learning. Lastly, it establishes that the correctly speciﬁed model is analytically robust, in that nearby misspeciﬁed models generate similar long-run beliefs.